GATE DA 2024 Set 1 — Question 10

MCQ+2 / -0.67MediumMensuration & GeometryQuantitative AptitudeGeneral Aptitude2D & 3D PatternsSpatial Aptitude

General Aptitude → Quantitative Aptitude → 2D & 3D Patterns

Last updated 5 September 2026

Question

Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make?

Correct answer (A) A rhombus Solution The assembled figure consists of two identical cones sharing a common circular base, with their vertices pointing in opposite directions (a bicone). A plane passing through both vertices cuts through the axis of symmetry. The cross-section of each cone through its vertex is an isosceles triangle. Since the cones are identical and share a base, the two triangles share a common base (the diameter of the circle) and are congruent. The union of these two triangles along their common base forms a quadrilateral with four equal sides (since the slant heights of identical right circular cones are equal). A quadrilateral with equal sides is a rhombus. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

Review answer and solution without JavaScript

Interactive answer checking needs JavaScript. The published solution is available below.

Correct answer (A) A rhombus Solution The assembled figure consists of two identical cones sharing a common circular base, with their vertices pointing in opposite directions (a bicone). A plane passing through both vertices cuts through the axis of symmetry. The cross-section of each cone through its vertex is an isosceles triangle. Since the cones are identical and share a base, the two triangles share a common base (the diameter of the circle) and are congruent. The union of these two triangles along their common base forms a quadrilateral with four equal sides (since the slant heights of identical right circular cones are equal). A quadrilateral with equal sides is a rhombus.

Continue learning with Success Tracker

Use Success Tracker to ask about the reasoning, then try another GATE DA question to check your understanding.

AI-powered practice· Unlimited practice on eligible plans

PYQs with solutions: Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
Practice that adapts: Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
AI doubt support: Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.

Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.

This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.